# Costing and Control System

CCS covers costing and refinement. The subject provides us tools for appropriate costing, breakevens and understanding variations.

## Breakeven point

$\text{Breakeven Point} = \dfrac{\text{FC}}{\text{Cost Margin Per Unit}} = \dfrac{FC}{SP-VC}$

For a given target profit-
$\text{Breakeven Point} = \dfrac{\text{FC + TP}}{\text{CMU}} = \dfrac{FC + TP}{SP-VC}$

## Variations

Total variations = Sales Variation + Cost Variation + Overhead Variation

## Sales Variation

Sales Variation
\begin{aligned} &= \Delta(\text{Contribution Margin per unit} * \text{Mix} * \text{Total}) \\ &= \Delta(BCM * M * T) \\ &= BCM * \Delta(MT) \\ &= \underbrace{BCM * \Delta M * AT}_{\text{Mix Variation}} + \underbrace{BCM * BM * \Delta T}_{\text{Quantity Variation}}\\ &= \text{Mix Variation} + BCM * BM * \Delta(\text{Market Size(MS)} * \text{Market Share(SH)}) \\ &= \text{Mix Variation} \\ &+ \underbrace{BCM * BM * \Delta MS * BSH}_{\text{Market Size Variation}} + \underbrace{BCM * BM * AMS * \Delta SH}_{\text{Market Share Variation}} \\ \end{aligned}

## Cost Variation

$Q_i$ - Quantity of individual material
$B$ - Budget
$BP$ - Budgeted price / Standard Price
$AP$ - Actual price
$BQ$ - Budgeted quantity
$AQ$ - Actual quantity
$M_A$ - Mix of A i.e ($Q_A/\Sigma_{a,b,c}Q_i$) i.e $Q_A/T_A$
$AM_A$ - Actual Mix of A i.e $AQ_A/AT_A$
$BM_A$ - Budgeted Mix of A i.e $BQ_A/BT_A$
$AT$ - Actual Total
$BT$ - Budgeted Total

$\Sigma_{a,b,c}Q_i$ - Sum of all quantites of materials in a given budget

\begin{aligned} Q_A &= M_A * \Sigma_{a,b,c}Q_i\\ B &= \Sigma_{a,b,c} (Q_A * P_A)\\ \\ \Delta B &= \underbrace{\Sigma_{a,b,c} (AQ_A * \Delta P_A)}_{\text{Price Variation}} + \underbrace{\Sigma_{a,b,c} (\Delta Q_A * BP_A)}_{\text{Usage Variation}} \\ \\ \Delta B &= \text{Price Variation} + \underbrace{\Sigma_{a,b,c} (\Delta (M_A * \Sigma_{a,b,c}Q_i)) * BP_A)}_{\text{Usage Variation}} \\ \\ \Delta B &= \text{Price Variation} + \underbrace{\Sigma_{a,b,c} (\Delta M_A * \Sigma_{a,b,c}AQ_i * BP_A)}_{\text{Mix Variation}} + \underbrace{\Sigma_{a,b,c} (BM_A * \Delta(\Sigma_{a,b,c}Q_i) * BP_A)}_{\text{Yield Variation}} \\ \\ \Delta B &= \text{Price Variation} + \text{Mix Variation} + \text{Yield Variation} \\ \\ \Delta B &= \text{Price Variation} + \underbrace{\Sigma_{a,b,c} ((BM_A-AM_A) * AT * BP_A)}_{\text{Mix Variation}} \\ &+ \underbrace{\Sigma_{a,b,c} (BM_A * (BT-AT) * BP_A)}_{\text{Yield Variation}} \end{aligned}